Averaging of semigroups associated to diffusion processes on a simplex

We study the averaging of a diffusion process living in simplex K Rn, n≥1. assume that its infinitesimal generator can be decomposed as sum two generators corresponding to distinct timescales and one fastest timescale is pure noise with coefficient vanishing exactly on vertices K. show this averages jump Markov for Meyer–Zheng topology. The role geometric assumptions done also discussed.